# Question: If X1 X2 Xn are independent and

If X1, X2, . . . ,Xn are independent and identically distributed random variables having uniform distributions over (0, 1), find

(a) E[max(X1, . . . ,Xn)];

(b) E[min(X1, . . . ,Xn)].

(a) E[max(X1, . . . ,Xn)];

(b) E[min(X1, . . . ,Xn)].

## Answer to relevant Questions

If 101 items are distributed among 10 boxes, then at least one of the boxes must contain more than 10 items. Use the probabilistic method to prove this result. In Problem 6, calculate the variance of the sum of the rolls. Problem 6 A fair die is rolled 10 times. Calculate the expected sum of the 10 rolls. The random variables X and Y have a joint density function given by Compute Cov(X, Y). If X1, X2, X3, and X4 are (pairwise) uncorrelated random variables, each having mean 0 and variance 1, compute the correlations of (a) X1 + X2 and X2 + X3; (b) X1 + X2 and X3 + X4. A prisoner is trapped in a cell containing 3 doors. The first door leads to a tunnel that returns him to his cell after 2 daysâ€™ travel. The second leads to a tunnel that returns him to his cell after 4 daysâ€™ travel. The ...Post your question